Does a square root have two values?
Last Updated :
13 Mar, 2024
Before finding does a square root has two values we must first know what are squares, square roots and others.
What is a Square?
Square of a number is defined as the value obtained by the multiplication of the number by itself. The exponential form of a square of a number x is written as x2.
For eg: Square of 2 is 22 = 2 × 2 = 4.
Square of a negative number is also a positive number. For eg: Square of -2 is (-2)2 = -2 × -2 = 4.
From the above two examples, it can be seen that the square of positive and negative numbers is always positive.
What is a Square Root?
Square Root of a number is the inverse operation of the square. If the square root of a number x is y, then the square of y is x. The exponential form of the square root is written as x-2. The square root of the number x is represented as √x.
For eg: Square Root of 25 is √25 = √(52) = 5.
Does a Square Root have Two Values?
Solution:
Square root of a number always has two answers, one is positive and one is negative. There are two answers because the square of a negative and positive number is the same.
For eg: Square of 3 is 9 and the square of -3 is also 9. So the square root of 9 is 3 and -3. Similarly, the square root of a number y is x and -x.
Similar Questions
Question 1: Calculate the square root of 36?
Solution:
Given number is 36
Write prime factors of 36
36 = 2 × 2 × 3 × 3
36 = 22 × 33
Now calculate the square root of the numbers.
√36 = √(22 × 32)
√36 = ±(2 × 3) = ±6
Hence, square root of the given number is 6 and -6
Question 2: Calculate the square root of 144?
Solution:
Given number is 144
Write prime factors of 144
144 = 2 × 2 × 2 × 2 × 3 × 3
144 = 24 × 32
Now calculate square root of numbers
√144 = √(24 × 32)
√144 = ±(4 × 3) = ±12
Hence, square root of the given number is 12 and -12
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